101 citations · 375 across the 39 of their papers we have counts for
42 papers
Differential Equations for Approximate Solutions of Painlevé Equations: Application to the Algebraic Solutions of the Painlevé-III Equation
Robert J. Buckingham, Peter D. Miller
It is well known that the Painlevé equations can formally degenerate to autonomous differential equations with elliptic function solutions in suitable scaling limits. A way to make…
Painlevé-III Monodromy Maps Under the Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions
Ahmad Barhoumi, Oleg Lisovyy, Peter D. Miller +1
The third Painlevé equation in its generic form, often referred to as Painlevé-III(), is given by $$ \frac{{\rm d}^2u}{{\rm d}x^2} =\frac{1}{u}\left(\frac{{\rm d}u}{{\rm d}x}\…
On the algebraic solutions of the Painleve-III (D7) equation
Robert J. Buckingham, Peter D. Miller
The D7 degeneration of the Painleve-III equation has solutions that are rational functions of for certain parameter values. We apply the isomonodromy method to obtain a R…
Broader Universality of Rogue Waves of Infinite Order
Deniz Bilman, Peter D. Miller
We show that the same special solution of the focusing nonlinear Schrödinger equation that has been shown to arise in a certain near-field/large-order limit from soliton and Peregr…
Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime
Deniz Bilman, Peter D. Miller
We study fundamental rogue-wave solutions of the focusing nonlinear Schrödinger equation in the limit that the order of the rogue wave is large and the independent variables $(x,t)…
Large-degree asymptotics of rational Painleve-IV solutions by the isomonodromy method
Robert J. Buckingham, Peter D. Miller
The Painleve-IV equation has two families of rational solutions generated respectively by the generalized Hermite polynomials and the generalized Okamoto polynomials. We apply the…